1. Field of the Invention
The invention relates to the field of automated facial recognition.
2. Description of the Related Art
Automated face recognition from video can be used for variety of applications. One known method for face recognition is the sparse representation-based (SRC) face recognition method. This method is based on the theory that the probe image (test sample) lies in the subspace spanned by the training images from the same class. By way of explanation, assume the i-th training class consists of ni training samplesAi=[Si,1,Si,2, . . . ,Si,ni].
If a new probe image y belongs to the subspace spanned by the i-th class, then:y=αi,1si,1+αi,2si,2+ . . . +αi,nisi,ni  (1)where αi,j are weight coefficients, j=1, . . . , n.
Since the membership of y is unknown, there can be built a training matrix A, where all the matrices for different training classes are concatenated together. If there are M total training classes, then the matrix is defined as:A=[A1,A2, . . . ,AM]=[s1,1,s1,2, . . . ,sM,nM]  (2)
From this, the reconstruction of y from the training images can be expressed by the following equation:y=Ax0  (3)where x0 is of the formx0=[0,0, . . . ,0,αi,1,αi,2, . . . ,0]i.e. only the coefficients corresponding the class that y belongs to are non-zero, all the others are zero. If the number of classes M is sufficiently large, the solution x0 is sparse. Hence, the sparsest solution to the following l1-minimization problem is sought:x1=arg min∥x∥1 s.t.Ax=y.  (4)
Here, ∥⋅∥1 represents the l1 norm.
For a probe image y, the solution xi is found by solving the above minimization problem. In an ideal case, only the coefficients corresponding to the representative class of probe image y will be non-zero. However, practical training datasets will have some inherent noise, and, hence, some non-representative coefficients will also have non-zero values. In order to classify a probe image, a reconstruction is sought for each class. For a solution x, Let δi(x) represents a vector in which only the coefficients corresponding to class i are kept from the entries of x, all the other entries are set to non-zero. Then, the reproduced probe image from only class i can be represented by Aδi(x). The residual ∥y−Aδi(x)∥ represents the reproduction error. y is assigned to the class that results in the minimum residue:miniri(y)=∥y−Aδi(x1)∥2  (5)
Instead of training a classifier and mapping the probe image through it as is done in some conventional training test paradigms, the SRC algorithm solves a minimization problem for every probe image. Due to the sparse nature of the solution, the occlusion, illumination and noise variations are also sparse in nature.